Steepness of a Line: Slope

Hi folks!

_{Special thanks to @jbeguna04 who made and design this header.}

Well, today allow me to share some sort of my knowledge regarding the basic mathematical problems from a topic that is being discussed and taught when studying for Mathematics. This topic is all about the steepness of a line, for which it is widely known to us as the slope. We must be thankful to Rene Descartes for conceptualizing analytic geometry which is also known as coordinate geometry, since for without it we would be having difficulties in solving basic problems in mathematics that can be represented thru points and be plotted thru the Cartesian coordinate system; and most importantly, if it didn't exist we wouldn't be able to witness some complex mathematical calculations which are being used in engineering, for example, doing simulations using highly advanced softwares such as does being deployed by ANSYS, whose computations are derived from theories in analytic geometry and in calculus.

Slope of a line is oftentimes described by educators as simply as rise over run. And is mathematical expressed in the photo shown below.

_{All screenshots made by me using Snipping Tool and the formula being made using the Equations feature in MS Word 2010 application.}

wherein;

• m is the slope of the line.
• x is the abscissa of an ordered pair.
• y is the ordinate of an ordered pair.

_{Note: The delta sign denotes change.}

Additionally, for easier comprehension to students, the best thing to remember when dealing with slope of a line is shown in the photo below. When the line is going to the upward to the right it is understood that the line is having a positive (+) slope; whereas if a line is going upward to the left, it is expected that the slope is having a negative (-) slope.

_{Image Source - By H Padleckas at English Wikibooks [Public Domain], via Wikimedia Commons}

This topic wouldn't be exciting if we don't a sample problem to show.
_{Actually I obtained this problem from @exillediogolvin's My Day in Facebook, wherein he shared this problem, and I took a screenshot of it and written in my notes. And it's the very reason I came up writing about slope of a line.}

The problem related to slope of a line is stated in this way;

A line with a slope of 1/5 passes through (6,2). If the abscissa on the line is 11, what is its ordinate?

Since we are provided with the slope of the line, the ordered pair of a point being passed by the line and we are provided also with the abscissa of an another point that is being passed by the line, and we are only asked for the ordinate, we will just simplify the general equation to obtain the value for y₂. And the computation is shown below.

In the above computation we've obtained the value of the ordinate as 3 (y₂ = 3).

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Additionally, we have another sample problem, this time around we are given with a negative slope.

Find y if the slope of the line segment joining (3,-2) to (4,y) is -3.

The same thing we do in the previous problem, we obtained the value of the ordinate as -5 (y₂ = -5).

Well, I guess that ends my first blog that tackles mathematics.

Thank you. Much love and respect.

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